Verified solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The first-order Macaulay ratio is (1.10/1.1025)¹¹ = 0.97534, so the approximate price change is −2.47%, choice B.
Independent solution
Setup
The yield increases from 10% to 10.25%, and the requested approximation uses Macaulay duration directly through the yield-factor ratio.
Model
Raise the old-to-new accumulation-factor ratio to the duration 11.
Compute
The resulting approximate price ratio is 0.97534, a decline of 0.02466.
Answer
Expressed as a percentage, the price change is about negative 2.47%, choice B.
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Error diagnosis
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Original practice · fully worked
A municipal arts instrument is worth 2000 and has modified duration 6.50. Its yield rises by 15 basis points. Using the first-order modified-duration approximation, estimate the new price.
The first-order relative change is -0.975%, giving price 1980.50, choice C.
Setup
Convert the basis-point movement to a decimal change in yield and retain the sign of the increase.
Model
Modified duration approximates the proportional price change as negative duration times the yield change.
Compute
The yield increase implies a proportional change of -0.00975000; applying it to 2000 gives 1980.50.
Answer
The estimated post-change price is 1980.50, which is choice C.
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ActuaryProof. “SOA Exam FM Sample Question #146 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
